We consider a family of discrete Jacobi operators on the one-dimensional integer lattice, with the diagonal and the off-diagonal entries given by two sequences generated by the Fibonacci substitution on two letters. We show that the spectrum is a Cantor set of zero Lebesgue measure, and discuss its fractal structure and Hausdorff dimension. We also extend some known results on the diagonal and the off-diagonal Fibonacci Hamiltonians.
Cite this article
William Yessen, Spectral analysis of tridiagonal Fibonacci Hamiltonians. J. Spectr. Theory 3 (2013), no. 1, pp. 101–128DOI 10.4171/JST/39